1. Field of the Invention
The present invention relates to an acceleration-detecting type gyro apparatus for use with navigation object, such as automobiles, ships or airplanes and which is used to detect angular velocity or angular change and acceleration relative to inertial space, and more particularly to a micro-acceleration-detecting type gyro apparatus in which a gyro rotor is floated and supported by an electrostatic supporting force.
2. Description of the Related Art
A gyro apparatus will be described with reference to FIGS. 1A, 1B through FIG. 7. Japanese patent application No. 6-136074, which had been filed on Jun. 17, 1994 by the same assignee of the present application, describes this type of gyro apparatus.
A structure of this gyro apparatus will be described with reference to FIGS. 1A, 1B. This gyro apparatus is referred to as an "electrostatic gyro", and includes a disk-like gyro rotor 20 floated and supported by an electrostatic supporting force, and a gyro case 21 with the gyro rotor 20 housed therein as shown in FIGS. 1A, 1B.
XYZ coordinates are set in this gyro apparatus as shown in FIGS. 1A, 1B. The Z axis is set upwardly along a central axis of the gyro apparatus, and the X axis and the Y axis are set at a right angle of the Z axis. A spin axis of the gyro rotor 20 is disposed along the Z axis.
The gyro case 21 comprises an upper bottom member 22, a lower bottom member 24, and a spacer 23 for coupling the upper and lower bottom members 22, 24. The upper and lower bottom members 22, 24 are connected by some suitable coupling means, such as small screws 25. In this manner, a disk-shaped rotor cavity 26 in which the gyro rotor 20 is housed is formed within the gyro case 21.
As shown in FIG. 1A, holes 22A, 22A' communicating with the rotor cavity 26 are defined on the upper bottom member 22 and the lower bottom member 24. A cap 32 is fitted into the hole 22A of the upper bottom member 22, and the cap 32 houses a getter 33 which is used in order to keep the rotor cavity 26 at high vacuum for a long period of time. A pipe 34 is connected to the hole 22A' of the lower bottom member 24, and the rotor cavity 26 is evacuated and kept vacuum through such pipe 34.
The gyro rotor 20 is made of a conductive material, and should preferably include, as shown in FIG. 1A, a thin central portion 20B, and a thick annular electrode portion 20C formed outside the thin central portion 20B. The central portion 20B has a through-hole 20A defined along the central axis.
The gyro apparatus includes a displacement detecting device for detecting a displacement of the gyro rotor 20 relative to the gyro case 21, and the displacement detecting device detects a radial displacement of the gyro rotor 20. The displacement detecting device includes a light-emitting device 27 and a light-receiving device 28 which are respectively disposed on the upper and lower surfaces of the inside of the rotor cavity 26 of the gyro case 21 as shown in FIG. 1A. The light-receiving device 28 is so-called quadrant light-receiving device composed of four segments 28-1, 28-2, 28-3, 28-4 as shown in FIG. 1B.
The light-emitting device 27 and the light-receiving device 28 are disposed at both sides of the through-hole 20A of the gyro rotor 20 in such a manner that a light path passes the through-hole 20A. When the gyro rotor 20 is displaced radially, the position of the through-hole 20A is deviated from the light path so that an amount of light received by the four segments 28-1 through 28-4 of the light-receiving device 28 from the light-emitting device 27 is changed. Changed amounts of light received by the four segments 28-1, 28-2, 28-3, 28-4 of the light-receiving device 28 are different, each segments being differentially wired. Hence, there can be obtained magnitude and direction of the radial displacement of the gyro rotor 20.
Electrostatic supporting electrodes 29-1 through 29-4 and rotor rotation driving coils 30-1 through 30-4 are concentrically disposed on the inner surface of the upper bottom member 22. Similarly, electrostatic supporting electrodes 29'-1 through 29'-4 and rotor rotation driving coils 30'-1 through 30'-4 are concentrically disposed on the inner surface of the lower bottom member 24. The electrostatic supporting electrodes 29-1 through 29-4 and 29'-1 through 29'-4 and the rotor rotation driving coils 30-1 through 30-4 and 30'-1 through 30'-4 are disposed in opposing relation to the electrode portion 20C of the gyro rotor 20 with a predetermined spacing between them and the electrode portion 20C. A positional relationship between the electrostatic supporting electrodes 29-1 through 29-4 and 29'-1 through 29'4 and the electrode portion 20C of the gyro rotor 20 will be described later on in detail.
As shown in FIG. 1B, the first electrostatic supporting electrode pair 29-1, 29'-1 and the third electrostatic supporting electrode pair 29-3, 29'-3 are disposed along the X axis, and the second electrostatic supporting electrode pair 29-2, 29'-2 and the fourth electrostatic supporting electrode pair 29-4, 29'-4 are disposed along the Y axis. The electrostatic supporting electrodes 29-1 through 29-4, and 29'-1 through 29'-4 are disposed among the rotor rotation driving coils 30-1 through 30-4 and 30'-1 through 30'-4. The electrostatic supporting electrodes 29-1 through 29-4, and 29'-1 through 29'-4 may be fan-shaped as shown in FIG. 1B.
The gyro rotor 20 is rotated at high speed about the Z axis on application of a drive AC voltage to the rotor rotation driving coils 30-1 through 30-4 and 30'-1 through 30'-4. Although the AC voltage is cut off when the rotational speed of the gyro rotor 20 reaches a desired rotational speed, the gyro rotor 20 is kept rotating by the force of inertia. Since the gyro rotor 20 is not in contact with and supported within the rotor cavity portion 26 of the gyro case 21 maintained at high vacuum, the gyro rotor 20 can keep rotating for several months or longer.
Because no extraneous torque acts on the gyro rotor 20, regardless of any movement of the gyro case 21, the spin axis direction of the gyro rotor 21 can be maintained in the constant direction relative to the inertial space.
Arrangements and operations of a Z-slaving control system, an XY-slaving control system and a rotor driving system mounted on the gyro apparatus will be described with reference to FIG. 2. The Z-slaving control system functions to slave a manner in which the gyro rotor 20 is displaced in the Z axis direction. Specifically, the Z-slaving control system functions to float and keep the gyro rotor 20 at a predetermined position. The XY-slaving control system functions to slave a manner in which the gyro rotor 20 is displaced in the XY-axis direction, and the rotor driving system 100 functions to rotate the gyro rotor 20 about the spin axis.
A first portion P1 assumes the electrode portion 20C of the gyro rotor 20 at its portion opposing the first electrostatic supporting electrode pair 29-1, 29'-1; a second portion P.sub.2 assumes the electrode portion 20C of the gyro rotor 20 at its portion opposing the second electrostatic supporting electrode pair 29-2, 29'-2; a third portion P.sub.3 assumes the electrode portion 20C of the gyro rotor 20 at its portion opposing the third electrostatic supporting electrode pair 29-3, 29'-3; and a fourth portion P.sub.4 assumes the electrode portion 20C of the gyro rotor 20 at its portion opposing the fourth electrostatic supporting electrode pair 29-4, 29'4.
Initially, arrangement and operation of the Z-slave control system will be described below. The Z-slave control system is of the electrostatic type, and therefore, the gyro rotor 20 is floated, supported, and slaved by an electrostatic force generated between the gyro rotor 20 and the electrostatic supporting electrodes.
The Z-slave control system includes the electrode portion 20C (portions P.sub.1, P.sub.3 in FIG. 2) of the gyro rotor 20, four pairs of electrostatic supporting electrodes 29-1, 29'-1, 29-2, 29'-2, 29-3, 29'-3, 29-4, 29'-4 (only the electrostatic supporting electrodes 29-1, 29'-1, 29-3, 29'-3 are shown in FIG. 2) disposed on both sides of the gyro rotor 20 and four transformers 41, 42, 43, 44 (only the transformers 41, 43 are shown in FIG. 2) connected to the electrostatic supporting electrodes 29-1, 29'-1, 29-2, 29'-2, 29-3, 29'-3, 29-4, 29'-4.
For the sake of simplicity, let it now be assumed that an X axis direction displacement .DELTA.x of the gyro rotor 20 and a Y axis direction displacement .DELTA.y of the gyro rotor 20 are both zero. As shown in FIG. 2, although an AC voltage (1.+-.K.sub.1 .DELTA.x) V.sub.TX corrected by the displacement .alpha.x is applied to junctions T1, T4 of the first and third transformers 41, 43, such coefficient is expressed by (1.+-.K.sub.1 .DELTA.x)=1. Accordingly, the AC voltage V.sub.TX with a reference frequency f.sub.0 is applied to the junctions T1, T4. output terminals T2, T3 of the first transformer 41 is connected to the electrostatic supporting electrodes 29-1, 29'-1, and output terminals T5, T6 of the third-transformer 43 are connected to the electrostatic supporting electrodes 29-3, 29'-3.
The first electrostatic supporting electrode pair 29-1, 29'-1 and the first portion P.sub.1 of the electrode portion 20C of the gyro rotor 20 constitute a capacitor (C is an electrostatic capacity), and such capacitor and the first transformer 41 (L is an inductance) constitute a resonance circuit. A resonance frequency f.sub.a =1/2.pi..sqroot.LC! of such resonance circuit is set to a value smaller than the reference frequency f.sub.0 of the AC voltage V.sub.TX applied to the first transformer 41.
Operation of the Z-slaving control system of the gyro apparatus will be described with reference to FIG. 3. FIG. 3 is a graph of a resonance curve, and to which reference will be made in explaining operation of the resonance circuit including the first transformer 41 and the electrostatic supporting electrodes 29-1, 29'-1 connected to the first transformer 41. In FIG. 3, the vertical axis represents an electrode voltage V.sub.T of one electrode, e.g., the electrostatic supporting electrode 29-1 disposed on the upper side of the gyro rotor 20, and the horizontal axis represents a frequency ratio (f.sub.0 /f.sub.a) wherein f.sub.0 is the reference frequency of the AC voltage V.sub.TX, and f.sub.a is the resonance frequency f.sub.a =1/2.pi..sqroot.LC! of the resonance circuit.
As described above, at the operation point, the resonance frequency f.sub.a of the resonance circuit is smaller than the reference frequency f.sub.0 of the AC voltage and the frequency ratio (f.sub.0 /f.sub.a) is larger than 1. Accordingly, as shown in FIG. 3, the electrode voltage V.sub.T is a decreasing function at the position near the operation point.
Let us consider the case that the first portion P.sub.1 of the electrode portion 20C of the gyro rotor 20 is displaced in the upper direction. In this case, a distance between the first portion P.sub.1 and the electrostatic supporting electrode 29-1 disposed above the first portion P.sub.1 is decreased, and hence the electrostatic capacity C between the first portion P.sub.1 and the electrostatic supporting electrode 29-1 is increased. Accordingly, the resonance frequency f.sub.a =1/2.pi..sqroot.LC! is decreased, and the frequency ratio (f.sub.0 /f.sub.a) is increased. As a consequence, as illustrated in FIG. 3, the electrode voltage V.sub.T of the electrostatic supporting electrode 29-1 becomes smaller than the operation voltage V.sub.T0. In this manner, an attraction generated between the upper electrostatic supporting electrode 29-1 and the first portion P.sub.1 of the gyro rotor 20 is decreased.
A relationship between the first portion P.sub.1 of the gyro rotor 20 and the electrostatic supporting electrode 29'-1 disposed under the first portion P.sub.1 becomes exactly opposite to the above-mentioned relationship. Specifically, the distance between the first portion P.sub.1 and the electrostatic supporting electrode 29'-1 disposed under the first portion P.sub.1 is increased, and the electrostatic capacity C between the first portion P.sub.1 and the electrostatic supporting electrode 29'-1 is decreased. Accordingly, the resonance frequency f.sub.a =1/2.pi..sqroot.LC! is increased, and hence the frequency ratio (f.sub.0 /f.sub.a) is decreased. As a result, the electrode voltage V.sub.T of the electrostatic supporting voltage 29'-1 becomes larger than the operation voltage V.sub.T0. In this manner, an attraction generated between the lower electrostatic supporting electrode 29'-1 and the first portion P.sub.1 of the gyro rotor 20 is increased.
When the first portion P.sub.1 of the gyro rotor 20 is displaced in the upper direction, a displacement force for displacing the first portion P.sub.1 in the upper direction is decreased, and a displacement force for displacing the first portion P.sub.1 of the gyro rotor 20 in the lower direction is increased. Therefore, the first portion P.sub.1 is displaced in the lower direction relatively, and operated so as to be returned to the original position.
According to the Z-slaving control system, the first resonance circuit including the first transformer 41 and the first electrostatic supporting electrode pair 29-1, 29'-1 constantly maintains the displacement of the Z axis direction of the first portion P.sub.1 of the electrode portion 20C of the gyro rotor 20 at zero, and the third resonance circuit including the third transformer 43 and the third electrostatic supporting electrodes 29-3, 29'-3 constantly maintains the displacement of the Z axis direction of the third portion P.sub.3 of the electrode portion 20C of the gyro rotor 20 at zero. Similarly, the second and fourth resonance circuits constantly maintains the displacements of the Z axis direction of the second and fourth portions P.sub.2, P.sub.4 of the electrode portion 20C of the gyro rotor 20 at zero.
A force Fz1 received at the first portion P.sub.1 of the gyro rotor 20 from the gyro case 21 is proportional to a difference between voltages A.sub.1 and B.sub.1 applied to the electrostatic supporting electrodes 29-1, 29'-1. Operation of the third portion P.sub.3 of the electrode portion 20C of the gyro rotor 20, and operations of the second and fourth portions P.sub.2, P.sub.4 are also similar to the operation of the first portion P.sub.1. EQU Fz1=K(A.sub.1 -B.sub.1) EQU Fz2=K(A.sub.2 -B.sub.2) EQU Fz3=K(A.sub.3 -B.sub.3) EQU Fz4=K(A.sub.4 -B.sub.4) (1)
Arrangement and operation of the rotor driving system 100 will be described with reference to FIG. 2.
As shown in FIG. 2, the rotor driving system includes the gyro rotor 20, the driving AC power supply 101, and four pairs of coils (only lower coils 30'-1, 30'-2, 30'-3, 30'-4 are illustrated in FIG. 2) connected to the driving AC power supply 101. A fundamental phase V.sub.0 of the 2-phase AC voltage is connected to the two coils 30'-1, 30'-3 connected in series, and a 90.degree.-phase V.sub.90 is connected to the two coils 30'-2, 30'-4 connected in series.
When an alternating voltage is applied to the four pairs of coils 30-1, 30'-1, 30-2, 30'-2, 30-3, 30'-3, 30-4, 30'-4, a rotation magnetic field proportional to the frequency of the driving AC power supply 101 is generated in the rotor cavity 26 of the gyro case 21, and the gyro rotor 20 is rotated by an interaction caused by the above magnetic field and an eddy current generated within the gyro rotor 20.
Arrangement and operation of the XY slaving control system of the gyro apparatus will be described with reference to FIGS. 4A, 4B. The XY slaving control system includes the displacement detecting apparatus comprising the electrode portion 20C of the gyro rotor 20, the electrostatic supporting electrodes 29-1 through 29-4, 29'-1 through 29'-4, the light-emitting device 27 and the light-receiving device 28, and X and Y control systems 50, 60 for receiving an output signal from the displacement detecting apparatus. The positions of the X axis and Y axis directions of the gyro rotor 20 are controlled in such a fashion that the spin axis is aligned with the central axis, i.e., Z axis of the gyro apparatus even when the gyro rotor 20 is displaced in the X-axis and Y-axis directions.
As shown in FIG. 4A, the X control system comprises an AC power supply 50-1 for supplying an AC voltage V.sub.T with a frequency f.sub.0, a V.sub.TX computing unit 50-2, and two multipliers 50-3, 50-4. The V.sub.TX computing unit 50-2 receives a signal indicative of a displacement .DELTA.x of the X axis direction of the gyro rotor 20 supplied from the light-receiving device 28 of the displacement detecting apparatus, and calculates a coefficient 1.+-.K.sub.1 .DELTA.x (K.sub.1 is a constant). One end of the AC power supply 50-1 is grounded and another end is connected to the two multipliers 50-3, 50-4. Therefore, the two multipliers 50-3, 50-4 output an AC voltage V.sub.T (1.+-.K.sub.1 .DELTA.x) corrected by the coefficient 1.+-.K.sub.1 .DELTA.x . As shown in FIG. 4B, arrangement of the Y control system 60 is similar to that of the X control system.
A positional relationship between the electrode portion 20C of the gyro rotor 20 and the electrostatic supporting electrodes 29-1 through 29-4 and 29'-1 through 29'-4 will be described below. Although the electrode portion 20C of the gyro rotor 20 is concentrically disposed relative to the electrostatic supporting electrodes 29-1 through 29-4 and 29'-1 through 29'-4, it is radially inwardly or outwardly displaced at the same time.
A manner in which the electrode portion 20 of the gyro rotor 20 is radially inwardly displaced from the electrostatic supporting electrodes 29-1 through 29-4 and 29'-1 through 29'-4 as shown in FIGS. 1A, 1B and FIG. 2 will be described. As illustrated, the outer diameters of the electrostatic supporting electrodes 29-1 through 29-4 and 29'-1 through 29'-4 are made larger than the outer diameter of the electrode portion 20C of the gyro rotor 20, and the electrostatic supporting electrodes 29-1 through 29-4 and 29'-1 through 29'-4 are radially outwardly protruded from the gyro rotor 20 by a length .delta..sub.2.
Further, the inner diameters of the electrostatic supporting electrodes 29-1 through 29-4 and 29'-1 through 29'-4 are made larger than the inner diameter of the electrode portion 20C of the gyro rotor 20, and the electrode portion 20C of the gyro rotor 20 is radially inwardly protruded from the electrostatic supporting electrodes 29-1 through 29-4 and 29'-1 through 29'-4 by a length .delta..sub.1.
The electrode portion 20C of the gyro rotor 20 is radially inwardly displaced from the electrostatic supporting electrodes 29-1 through 29-4 and 29'-1 through 29'-4, whereby the first electrostatic supporting electrode pair 29-1, 29'1 cause a force Fx1 to act radially outwardly on the gyro rotor 20 (positive direction of X axis), and the third electrostatic supporting electrode pair 29-3, 29'-3 cause a force Fx3 to act radially outwardly on the gyro rotor 20 (negative direction of X axis). These forces Fx1, Fx3 are changed in magnitude depending on the magnitudes of the AC voltages applied to the junctions T1, T4 of the first and fourth transformers 41, 44. As long as such AC voltages are equal, the two forces Fx1, Fx3 are balanced equally.
When an X-axis direction acceleration .alpha..sub.x acts on the gyro rotor 20, the gyro rotor 20 is displaced from the gyro case 21 by .DELTA.x in the positive direction of X axis. The above displacement .DELTA.x is outputted from the light-receiving device 28 as a voltage signal. The voltage signal is supplied to the V.sub.TX computing unit 50-2 of the X control system 50 and thereby the signal indicative of the coefficient 1.+-.K.sub.1 .DELTA.x is generated. Thus, two multipliers 50-3, 50-4 generate different voltage signals (1-K.sub.1 .DELTA.x)V.sub.T, (1+K.sub.1 .DELTA.x)V.sub.T.
The voltage signals (1.+-.K.sub.1 .DELTA.x)V.sub.T are applied to the junctions T1, T4 of the two transformers 41, 43, whereby the first electrostatic supporting electrode pair 29-1, 29'-1 generate the force Fx1 and the third electrostatic supporting electrode pair 29-3, 29'-3 generate the force Fx3. The force Fx1 acting on the gyro rotor 20 in the positive direction of X axis and the force Fx3 acting on the gyro rotor 20 in the negative direction of X axis are expressed by the equation (2) below: EQU Fx1=k.sub.1 (1-K.sub.1 .DELTA.x)V.sub.T EQU Fx3=k.sub.1 (1+K.sub.1 .DELTA.x)V.sub.T ( 2)
where k.sub.1 is the constant. A resultant force of X-axis direction forces acting on the gyro rotor 20 is expressed by the following equation (3): EQU Fx1-Fx3=-2k.sub.1 K.sub.1 V.sub.T .multidot..DELTA.x (3)
The gyro rotor 20 is pulled in the negative direction of X axis by the force proportional to the displacement .DELTA.x as expressed by the equation (3), and thereby the displacement of the gyro rotor 20 is canceled out. This is also true when the gyro rotor 20 is displaced in the Y axis direction. In this manner, even when the gyro rotor 20 is displaced in the X-axis and Y-axis directions by the XY slaving control system, the displacement amounts .DELTA.x and .DELTA.y are constantly held at zero. Specifically, the spin axis of the gyro rotor 20 is constantly aligned with the central axis, i.e., Z axis of the gyro apparatus.
Although it was assumed that the changed amounts of the voltages applied to the junctions T1, T4 of the two transformers 41, 43 are proportional to the displacement .DELTA.x, the voltages actually applied to the two junctions T1, T4 contain a term K.sub.D (d.DELTA.x/dt)V.sub.T caused by damping in addition to the term K.sub.1 .DELTA.xV.sub.T proportional to the displacement .DELTA.x.
While a manner in which the electrode portion 20C of the gyro rotor 20 is radially inwardly displaced from the electrostatic supporting electrodes 29-1 through 29-4 and 29'-1 through 29'-4 has been described so far with reference to FIGS. 1A, 1B and FIG. 2, if the electrode portion 20C of the gyro rotor 20 is radially outwardly displaced from the electrostatic supporting electrodes 29-1 through 29-4 and 29'-1 through 29'-4, then similar operation is carried out. However in that case, the directions of the forces Fx1, Fx3 acting on the gyro rotor 20 are reversed. Furthermore, this is also true when the acceleration .alpha.y of the Y-axis direction acts on the gyro rotor 20 so that the gyro rotor 20 is displaced from the gyro case by .DELTA.y in the Y-axis direction.
Arrangements and operations of a gyro computing unit and an acceleration computing unit will be described with reference to FIGS. 5A, 5B through FIG. 7. A gyro computing unit includes an X gyro computing unit for computing an angular velocity d.phi./dt around X axis and a Y gyro computing unit 61 for computing an angular velocity d.theta./dt around Y axis. An acceleration computing unit includes an X acceleration computing unit 53 for computing an X-axis direction acceleration, a Y acceleration computing unit 63 for computing a Y-axis direction acceleration, and a Z acceleration computing unit 73 for computing a Z-axis direction acceleration.
Arrangements and operations of the X gyro computing unit 51 and the X acceleration computing unit 53 will be described with reference to FIGS. 5A, 5B. As shown in FIG. 5A, the X gyro computing unit 51 includes four voltage-dividing units 51-1 through 51-4, four rectifying units 51-5 through 51-8 connected to each of the voltage-dividing units 51-1 through 51-4, two subtraction units 51-9, 51-10 connected to two pairs of rectifying units 51-5, 51-6 and 51-7, 51-8, and third computing units 51-11, 51-12 connected to the two subtraction units 51-9, 51-10.
The X gyro computing unit 51 receives terminal outputs A.sub.1, B.sub.1 and A.sub.3, B.sub.3 outputted from the output terminals T2, T3, T5, T6 of the two transformers 41, 43 through input terminals 51a, 51b and 51c, 51d. Because the terminal outputs A.sub.1, B.sub.1 and A.sub.3, B.sub.3 developed at the output terminals T2, T3 and T5, T6 of the two transformers 41, 43 are generally high voltages higher than 1000 V, such voltages are divided to low voltages by the four voltage-dividing units 51-1 through 51-4, and rectified as DC voltages by the four rectifying units 51-5 through 51-8. The DC voltage signals are subtracted by the subtraction units 51-9, 51-10, 51-11, and hence a gyro signal indicative of a rotation angular velocity d.phi./dt around X axis of the gyro rotor 20 is outputted from the output terminal of the computing unit 51-12.
Operation of the X gyro computing unit 51 will be described in detail. Let us consider that the angular velocity d.phi./dt is inputted around the X axis. An angular momentum vector H obtained by the spin motion of the gyro rotor 20 is oriented in the upper direction along the Z axis as shown in FIG. 2. The spin axis of the gyro rotor 20 is caused to keep being disposed along the Z axis direction due to law of inertia. When on the other hand the gyro case 21 is displaced around the X axis at the angular velocity d.phi./dt, the second electrostatic supporting electrode pair 29-2, 29'-2 and the fourth electrostatic supporting electrode pair 29-4, 29'-4 generate differences in the clearances between the second and fourth portions P.sub.2, P.sub.4 of the gyro rotor 20 and the upper and lower electrodes. Such differences between the upper and lower clearances are canceled out by the operation of the Y control system 60. At that very time, the two opposite forces Fz2, Fz4 are caused to act on the second and fourth portions P.sub.2, P.sub.4 of the gyro rotor 20 along the Z axis, whereby a torque T.sub.X expressed by the following equation (4) is generated. EQU T.sub.X =(Fz2-Fz4).multidot.r (4)
where r is the distance from the spin axis to a point at which force acts on the gyro rotor 20.
The torque T.sub.X causes the spin axis of the gyro rotor 20 to make a precession around the Y axis at a small angle. The precession of the spin axis causes the clearances between the first electrostatic supporting electrode pair 29-1, 29'-1, the third electrostatic supporting electrode pair 29-3, 29'-3 and the first and third portions P.sub.1, P.sub.3 of the gyro rotor 20 to be changed, i.e., a difference is generated between the upper and lower clearances.
Similarly, the differences between the upper and lower clearances are canceled by the operation of the X control system 50. At that very time, the two opposite forces Fz1, Fz3 act on the first and third portions P.sub.1, P.sub.3 of the gyro rotor 20 thereby to generate a torque T.sub.Y expressed by the following equation (5): EQU T.sub.Y =(fz1-Fz3).multidot.r (5)
The torque T.sub.Y causes the spin axis of the gyro rotor 20 to make a precession around the X axis at a small angle. Such precession becomes the same motion caused by the input angular velocity d.phi./dt. As a consequence, the spin axis and the gyro case 21 are rotated around the X axis at the angular velocity d.phi./dt in unison with each other.
Establishing an angular momentum equation based on the equations (4), (5) and using the equation (1), then we have: EQU H(d.phi./dt)=(Fz3-Fz1).multidot.r=(A.sub.3 -B.sub.3)-(A.sub.1 -B.sub.1)!.multidot.r.multidot.K EQU H(d.theta./dt)=(Fz4-Fz2).multidot.r=(A.sub.4 -B.sub.4)-(A.sub.2 -B.sub.2)!.multidot.r.multidot.K (6)
where H is the angular momentum amount of the gyro rotor 20. Thus, we have: EQU d.phi./dt=(A.sub.3 -B.sub.3)-(A.sub.1 -B.sub.1)!.multidot.Kr/H EQU d.theta./dt=(A.sub.4 -B.sub.4)-(A.sub.2 -B.sub.2)!.multidot.Kr/H(7)
In this manner, the X gyro computing unit 51 and the Y gyro computing unit 53 receive the terminal outputs A.sub.1, B.sub.1, A.sub.2, B.sub.2, A.sub.3, B.sub.3, A.sub.4, B.sub.4 of the four transformers, and output the X gyro signal d.phi./dt and the Y gyro signal d.theta./dt.
Arrangement and operation of the X acceleration computing unit 53 will be described below. The X acceleration computing unit 53 includes an adding unit 53-1 for receiving output signal a.sub.1, b.sub.1 of the first pair of rectifying units 51-5, 51-6 of the X gyro computing unit 51, an adding unit 53-2 for receiving output signals a.sub.3, b.sub.3 of the second pair of rectifying units 51-7, 51-8 and a subtraction unit 53-3 connected to the above-mentioned two adding units 53-1, 53-2.
The adding units 53-1, 53-2 calculate sums a.sub.1 +b.sub.1, a.sub.3 +b.sub.3 of the inside outputs of the X gyro computing unit 51, and the above sums correspond to sums A.sub.1 +B.sub.1, A.sub.3 +B.sub.3 of the voltages applied to the respective electrodes. Therefore, the outputs of the adding units 53-1, 53-2 correspond to the forces Fx1, Fx3 of the X axis direction.
The subtraction unit 53-3 calculates a difference (a.sub.1 +b.sub.1)-(a.sub.3 +b.sub.3) of outputs a.sub.1 +b.sub.1, a.sub.3 +b.sub.3 of the adding units 53-1, 53-2, and such difference corresponds to (A.sub.1 +B.sub.1)-(A.sub.3 +B.sub.3). Therefore, the output of the subtracting unit 53-3 corresponds to a difference between the force Fx1 of positive direction of X axis and a force Fx3 of negative direction of X axis.
In this manner, the subtraction unit 53-3 outputs the signal indicative of the displacement .DELTA.x expressed by the equation (3), and thereby the acceleration .alpha..sub.x is obtained.
Arrangements and operations of the Y gyro computing unit 61 and the Y acceleration computing unit 63 shown in FIGS. 6A, 6B are similar to those of the X gyro computing unit 51 and the X acceleration computing unit 53 shown in FIGS. 5A, 5B, and therefore need not be described.
Arrangement and operation of the Z acceleration computing unit 73 will be described with reference to FIG. 7. The Z acceleration computing unit 73 receives the internal signals a.sub.1, b.sub.1, a.sub.3, b.sub.3 of the X gyro computing unit 51 and the internal signals a.sub.2, b.sub.2, a.sub.4, b.sub.4 of the Y gyro computing unit 61, and calculates the acceleration of Z axis direction.
Operation of the Z acceleration computing unit 73 will be described. Although the acceleration is calculated under the assumption that the mass of the gyro rotor 20 is zero as described above, the mass of the gyro rotor 20 is not zero in actual practice. Accordingly, m assumes the mass of the gyro rotor 20, and divided into four portions. Assuming now that an acceleration az acts in the Z axis direction, then forces Fz1, Fz3 acting on the first and third portion P.sub.1, P.sub.3 of the gyro rotor 20 are expressed by the following equation (8): EQU Fz1=m.alpha..sub.z /4-(H/r) (d.phi./dt) EQU Fz3=m.alpha..sub.z /4+(H/r) (d.phi./dt) (8)
Computing sums of the above two equations, we can compute the acceleration .alpha..sub.z of Z axis direction as: EQU .alpha..sub.z =(Fz1+Fz3).multidot.2/m=(A.sub.3 -B.sub.3)+(A.sub.1 -B.sub.1)!.multidot.2K/m (9)
Incidentally, the acceleration .alpha..sub.z of Z axis direction can also be obtained by forces Fz2, Fz4 acting on the second and fourth portions P.sub.2 and P.sub.4 of the gyro rotor 20. Therefore, the Z acceleration computing unit 73 computes the acceleration az of Z axis direction from the four forces Fz1, Fz2, Fz3, Fz4 acting on the respective portions of the gyro rotor 20.
As earlier noted with reference to FIGS. 2, 3, and FIGS. 4A, 4B, the Z slaving control system and the XY slaving control system of the gyro apparatus constantly maintain the displacements of the gyro rotor 20 in the Z axis direction and XY axis direction at zero by use of the LC resonance circuit. In the first portion P.sub.1 of the electrode portion 20C of the gyro rotor 20, for example, the system including the AC power supply 50-1 of the X slaving control system 50, the transformer 41 and the first electrostatic supporting electrode pair 29-1, 29'-1 constructs the LC resonance circuit.
The Z slaving control system and the XY slaving control system using the LC resonance circuit unavoidably generate various errors in the path from the power supply to the gyro rotor 20, and in the path from the AC power supply 50-1 to the gyro rotor 20 through the transformer 41 and the first electrostatic supporting electrodes 29-1, 29'-1. One of such errors is a stray capacity caused by large size of coils and interconnections.
Further, in the Z, XY slaving control systems, when a floating force or restoration force for the gyro rotor 20 is adjusted, the coefficient 1.+-.K.sub.1 .DELTA.x of the V.sub.TX computing unit 50-2 has to be changed, and hence the operation therefor becomes cumbersome. In particular, it is difficult to float the gyro rotor 20 when the gyro apparatus starts up.